scholarly journals Normal approximations for discrete-time occupancy processes

2020 ◽  
Vol 130 (10) ◽  
pp. 6414-6444
Author(s):  
Liam Hodgkinson ◽  
Ross McVinish ◽  
Philip K. Pollett
Keyword(s):  
Discrete Time ◽  
Normal Approximations

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

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